Question: How many numbers between $1$ and $100$ (inclusive) are divisible by $5$ or $8$ ?
There are $20$ numbers divisible by $5$ between $1$ and $100$, and $12$ numbers divisible by $8$ between $1$ and $100$. So, you might think there are $20 + 12 = 32$ numbers divisible by one or the other, but this is overcounting something. We're counting every number which is divisible by both $5$ and $8$ twice. So, for example, $40$ is counted once as a number divisible by $5$, and then again as a number divisible by $8$. So, we need to count how many numbers are divisible by both $5$ and $8$ and subtract this from what we had before. Being divisible by both $5$ and $8$ is the same thing as being divisible by $40$, so there are $2$ numbers between $1$ and $100$ divisible by both. Subtracting, there are $32 - 2 = 30$ numbers divisible by $5$ or $8$.